신다 is the verb for putting on shoes and socks specifically — clothing takes 입다 instead, and mixing them up is a common mistake. 갈아 신다, changing into another pair, is what five of these lines are about: aqua shoes, gym trainers, black Uggs. 바꿔 신다 is swapping pairs with someone else and 꺾어 신다 is treading the back of the shoe down.